How do I find a DE that is consistent with:
$\displaystyle u_j^{n+1}=\frac{1}{2}(u_{j+1}^n+u_{j-1}^n)-\frac{1}{2}\frac{\Delta t}{(\Delta x)^3}(u_{j+2}^n-2u_{j-1}^n-u_{j-2}^n)$
Also, when is the scheme stable?
How do I find a DE that is consistent with:
$\displaystyle u_j^{n+1}=\frac{1}{2}(u_{j+1}^n+u_{j-1}^n)-\frac{1}{2}\frac{\Delta t}{(\Delta x)^3}(u_{j+2}^n-2u_{j-1}^n-u_{j-2}^n)$
Also, when is the scheme stable?